Scale space implementation

Abstract: This paper discusses the application of the windowed fast Fourier transform to electric power quality assessment. The windowed FFT is a time windowed version of the discrete time Fourier transform. The window width may be adjusted and shifted to scan through large volumes of power quality data. Narrow window widths are used for detailed analyses, and wide window widths are used to move rapidly across archived power quality data measurements. The mathematics of the method are discussed and applications are illustrated.

Abstract: The multiplicative transfer function (MTF) approximation is widely used for modeling a linear time invariant system in the short-time Fourier transform (STFT) domain. It relies on the assumption of a long analysis window compared with the length of the system impulse response. In this paper, we investigate the influence of the analysis window length on the performance of a system identifier that utilizes the MTF approximation. We derive analytic expressions for the minimum mean-square error (MMSE) in the STFT domain and show that the system identification performance does not necessarily improve by increasing the length of the analysis window. The optimal window length, that achieves the MMSE, depends on the signal-to-noise ratio and the length of the input signal. The theoretical analysis is supported by simulation results

Abstract: A frequency analysis method comprises using a window function to evaluate aemporal input signal present in the form of discrete sampled values. The windowed input signal is subsequently subjected to Fourier transformation for the purpose of generating a set of coefficients. In order to develop such a method so that the characteristics of the human ear are simulated not only with respect to the spectral projection in the frequency range, but also with respect to the resolution in the temporal range, a set of different window functions is used to evaluate a block of the input signal in order to generate a set of blocks, weighted with the respective window functions, of sampled values whose Fourier transforms have different bandwidths, before each of the simultaneously generated blocks of sampled values is subjected to a dedicated Fourier transformation in such a way that for each window function at least respectively one coefficient is calculated which is assigned the bandwidth of the Fourier transforms of this window function, and that the coefficients are chosen such that the frequency bands assigned to them essentially adjoin one another.

Abstract: A class of window functions is introduced for designing FIR filters. These window functions are obtained from the rectangular window by using a simple frequency transformation. The frequency transformation contains an adjustable parameter with which the mainlobe width and, correspondingly, the minimum stopband attenuation of the resulting filter can be controlled. The transition bandwidth of the filter can then be controlled by the filter order. Like the well-known Kaiser window, the proposed windows are close approximations to the discrete prolate functions which minimize the sidelobe energy. The FIR filters obtained by using the new window are slightly better than those obtained by using the Kaiser window. The main advantages of the proposed window compared to the Kaiser window are that the new window possesses analytic expressions in both the time and frequency domains and no power series expansions are required in evaluating the window function. Furthermore, it provides a better approximation to the discrete prolate functions. >